The gas mileages (in miles per gallon) for 32 cars are shown in the frequency distribution. Approximate the mean of the frequency distribution Frequenc Gas Mileage (in miles per gallon) 25 29 3034 35 39 40 44 The approximate mean of the frequency distribution is (Round to one decimal place as needed.)

Answer:220

Step-by-step explanation:88/4=22 x 10= 220

The given expression is proved by the necessary changes.

cosec 2A + cosec 4A = cot A - cot 4A​

Cosec 2 A + Cot 4 A = Cosec 4 A - Cot 2 A

Taking LHS  :

⇒Cosec 2 A + Cot 4 A

⇒Cosec 2 A + ( Cot 2 A )2

⇒Cosec 2 A + ( Cosec 2 A - 1 )2    (  we know:1+ Cot 2 θ =  Cosec 2 θ )

⇒Cosec 2 A +  Cosec 4 A  + 1  - 2 Cosec 2 A

⇒ Cosec 4 A  + 1  - Cosec 2 A

⇒ Cosec 4 A  + 1  - ( 1 + Cot 2 A)

⇒ Cosec 4 A  + 1  -  1 - Cot 2 A

⇒ Cosec 4 A  - Cot 2 A

or cosec2A+cosec4A=cotA-cot4A

Hence Proved.

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Let x = the number of games. The problem can be rewritten as a system of equations:

Person 1 = 72.48 + 6x

Person 2 = 18.08x

We are looking for when the number of games for both are the same; so:

72.48 + 6x = 18.08x

Then:

72.48 = 18.08x - 6x

72.48 = 12.08x

x = 72.48/12.08

x = 6

Answer:

36

Step-by-step explanation:

Same side

Answer:

Step-by-step explanation:

a is supplementary with 36 and b is supplementary with 113. Same side interior angles.

Supplementary angles sum to 180°

Answer:

A. 1

Step-by-step explanation:

Since it's g(-4), we have to use the first option because that means that x is equal to less than -4.

3√x + 5

3 √-4 + 5

= 1

Answer:

x = -√½ or √⁹/₁₀

Step-by-step explanation:

x + √(1 − x²) = √(2(2x² − 1))

Square both sides:

x² + 2x√(1 − x²) + 1 − x² = 2(2x² − 1)

2x√(1 − x²) + 1 = 4x² − 2

2x√(1 − x²) = 4x² − 3

Square both sides again:

4x² (1 − x²) = 16x⁴ − 24x² + 9

4x² − 4x⁴ = 16x⁴ − 24x² + 9

0 = 20x⁴ − 28x² + 9

Solve with quadratic formula:

x² = [ 28 ± √(28² − 4(20)(9)) ] / 2(20)

x² = (28 ± 8) / 40

x² = ½, ⁹/₁₀

x = ±√½, ±√⁹/₁₀

Check for extraneous solutions.

If x = -√½:

-√½ + √(1 − ½) = √(2(2(½) − 1))

-√½ + √½ = √(2(1 − 1))

0 = 0

If x = √½:

√½ + √(1 − ½) = √(2(2(½) − 1))

√½ + √½ = √(2(1 − 1))

√2 = 0

If x = -√⁹/₁₀:

-√⁹/₁₀ + √(1 − ⁹/₁₀) = √(2(2(⁹/₁₀) − 1))

-√⁹/₁₀ + √¹/₁₀ = √(2(⁹/₅ − 1))

-√⅖ = √⁸/₅

If x = √⁹/₁₀:

√⁹/₁₀ + √(1 − ⁹/₁₀) = √(2(2(⁹/₁₀) − 1))

√⁹/₁₀ + √¹/₁₀ = √(2(⁹/₅ − 1))

√⁸/₅ = √⁸/₅

Answer:

x = -77

Step-by-step explanation:

based on the given conditions

x - 14 = -91

x = -91 + 14 then calculate the difference between -91 - 14 = -77

thus x which is peters number = -77

We have proved that Angle BCD is equal to angle BAD plus angle ABC plus angle ADC, as required.

To prove that angle BCD is equal to angle BAD plus angle ABC plus angle ADC, we can use the following steps:

Step 1: Join points A and C with a line segment. Let's label the point where AC intersects with line segment BD as point E.

Step 2: Since line segment AC is drawn, we can consider triangle ABC and triangle ADC separately.

Step 3: In triangle ABC, we have angle B + angle ABC + angle BCA = 180 degrees (due to the sum of angles in a triangle).

Step 4: In triangle ADC, we have angle D + angle ADC + angle CDA = 180 degrees.

Step 5: From steps 3 and 4, we can deduce that angle B + angle ABC + angle BCA + angle D + angle ADC + angle CDA = 360 degrees (by adding the equations from steps 3 and 4).

Step 6: Consider quadrilateral ABED. The sum of angles in a quadrilateral is 360 degrees.

Step 7: In quadrilateral ABED, we have angle BAD + angle ABC + angle BCD + angle CDA = 360 degrees.

Step 8: Comparing steps 5 and 7, we can conclude that angle B + angle BCD + angle D = angle BAD + angle ABC + angle ADC.

Step 9: Rearranging step 8, we get angle BCD = angle BAD + angle ABC + angle ADC.

Therefore, we have proved that angle BCD is equal to angle BAD plus angle ABC plus angle ADC, as required.

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Given: Quadrilateral \(\displaystyle\sf ABCD\)

To prove: \(\displaystyle\sf \angle BCD = \angle BAD + \angle ABC + \angle ADC\)

Proof:

1. Draw segment \(\displaystyle\sf AC\) and extend it to point \(\displaystyle\sf E\).

2. Consider triangle \(\displaystyle\sf ACD\) and triangle \(\displaystyle\sf BCE\).

3. In triangle \(\displaystyle\sf ACD\):

4. In triangle \(\displaystyle\sf BCE\):

5. Since \(\displaystyle\sf \angle BCE\) and \(\displaystyle\sf \angle BCD\) are corresponding angles formed by transversal \(\displaystyle\sf BE\):

6. Combining the equations from steps 3 and 4:

Therefore, we have proven that in quadrilateral \(\displaystyle\sf ABCD\), \(\displaystyle\sf \angle BCD = \angle BAD + \angle ABC + \angle ADC\).

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

Answer:

Step-by-step explanation:

I think it is solve for a

a / 5 = ap + q

a(1/5 - p) = q

a(1 - 5p) = 5q

a = 5q / (1 - 5p)

Answer:

it is option D

2 less than 5 times a number

hope it helps

We have a problem of a sysmtem of equation

x is the number tickets sold of general admission

y is the number o tickets sold for seniors

The first equation is about the number of ticktes sold

x+y=155

the second equation is about the amount of money

12x+9y=1680

we isolate x of the first equation

x=155-y

we substitute the equatio above in the second equation

12(155-y)+9y=1680

1860-12y+9y=1680

we isolate the y

-3y=1680-1860

-3y=-180

y=-180/-3

y=60

then we substitute the value of y in order to find x

x=155-y

x=155-60

x=95

They sold 95 tickets of general admission

Hope you could understand.

If you have any query, feel free to ask.

Expanding the given expression and substituting the given values of \(\dfrac{p}{q}\) with \(\dfrac{q}{r}\) proves that the given equation

Correct response:

\(The \ expression \ p^3 + q^3 + r^3 \ is \ equal \ to \ \left(\dfrac{1}{p^3} + \dfrac{1}{q^3} +\dfrac{1}{r^3} \right) \cdot p^2 \cdot q^2 \cdot r^2 \ by \ subtituting\)

\(\dfrac{p}{q} = \dfrac{q}{r}\)

The given relation is;

\(\dfrac{p}{q} = \mathbf{\dfrac{q}{r}}\)

The given equation is presented as follows;

\(p^3 + q^3 + r^3 = \mathbf{\left(\dfrac{1}{p^3} + \dfrac{1}{q^3} + \dfrac{1}{r^3} \right) \cdot p^2 \cdot q^2 \cdot r^2}\)

Expanding the right hand side gives;

\(\dfrac{p^2 \cdot q^2 \cdot r^2}{p^3} + \dfrac{p^2 \cdot q^2 \cdot r^2}{q^3} + \dfrac{p^2 \cdot q^2 \cdot r^2}{r^3} = \mathbf{ \dfrac{q^2 \cdot r^2}{p} + \dfrac{p^2 \cdot r^2}{q} + \dfrac{p^2 \cdot q^2 }{r}}\)

\(\dfrac{q^2 \cdot r^2}{p} + \dfrac{p^2 \cdot r^2}{q} + \dfrac{p^2 \cdot q^2 }{r} = \mathbf{ \dfrac{q}{p} \cdot q \cdot r^2 + \dfrac{p}{q} \cdot p \cdot r^2+\dfrac{q}{r} \cdot p^2 \cdot q }\)

\(\dfrac{q}{p} \cdot q \cdot r^2 + \dfrac{p}{q} \cdot p \cdot r^2+\dfrac{q}{r} \cdot p^2 \cdot q } = \dfrac{r}{q} \cdot q \cdot r^2 + \dfrac{q}{r} \cdot p \cdot r^2+\dfrac{p}{q} \cdot p^2 \cdot q } = \mathbf{ r^3 + q \cdot p \cdot r + p^3}\)

From the given relation, we have;

p·r = q²

Therefore;

q·p·r = q × q² = q³

Which gives;

r³ + q·p·r + p³ = r³ + q³ + p³

Which gives;

\(\left(\dfrac{1}{p^3} + \dfrac{1}{q^3} + \dfrac{1}{r^3} \right) \cdot p^2 \cdot q^2 \cdot r^2 = p^3 + q^3 + r^3\)

By symmetric property, therefore;

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Answer:

option d

corresponding

The correct statements regarding activity diagrams are:

a. There can be multiple end points, but only one starting point.

c. A branch can have multiple incoming arrows.

d. A decision point may have more than 2 outgoing arrows.

e. An indeterminacy is created when the successors of an activity have non-mutually exclusive conditions.

f. An activity can be nested within another activity.

Activity diagrams are graphical representations used in software engineering to depict the flow of activities or actions within a system. The correct statements regarding activity diagrams are as follows:

a. There can be multiple end points, but only one starting point:

Activity diagrams typically illustrate the flow of activities from a single starting point to multiple end points. This allows for depicting different termination points in the system's behavior.

c. A branch can have multiple incoming arrows:

A branch in an activity diagram represents a decision point where the flow of activities can diverge. It is possible for multiple incoming arrows to converge at a branch, indicating different paths leading to the decision point.

d. A decision point may have more than 2 outgoing arrows:

A decision point in an activity diagram represents a condition or a decision that determines the subsequent flow of activities. It is possible for a decision point to have more than two outgoing arrows, indicating different paths based on the decision outcome.

e. An indeterminacy is created when the successors of an activity have non-mutually exclusive conditions:

In an activity diagram, if the subsequent activities following a certain action have conditions that are not mutually exclusive, it creates an indeterminacy. This means that multiple paths may be followed simultaneously based on the different conditions.

f. An activity can be nested within another activity:

Activity diagrams support the nesting of activities within each other. This allows for representing complex activities or sub-processes within a larger activity, providing a hierarchical structure to the diagram.

In conclusion, the correct statements regarding activity diagrams include multiple end points and a single starting point, the possibility of multiple incoming arrows at a branch, the presence of more than two outgoing arrows at a decision point, the creation of indeterminacy with non-mutually exclusive conditions, and the ability to nest activities within one another.

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We are interested in the activity diagram. Check all the correct answers.

Please select at least one answer.

O a. There can be multiple end points, but only one starting point.

O b. Any joint must have been preceded by a branch.

O c. A branch can have multiple incoming arrows.

O d. A decision point may have more than 2 outgoing arrows.

Oe. An indeterminacy is created when the successors of an activity have non-mutually exclusive conditions.

Of. An activity can be nested within another activity.

Answer: 620≥ 427.57+ 11.38(4)+ (31.41) +57.75x

Step-by-step explanation:

So our limit is the 620$ that he has to spend. We know for a fact that the bike costs about 427.57 dollars. 4  $11.38 reflectors are purchased as well as gloves for 31.41.  Now however many outfits he can purchase cannot exceed or go over his money limit of 620 so the variable (x) represents how many outfits he can buy without going over.

We are required to write an inequality for the problem and also solve it

The number of biking outfit Ethan can purchase is 2

Given:

Total amount Ethan has = $620

Amount of bicycle = $427.57

Bicycle reflector = $11.38

Cost of 4 Bicycle reflector = $11.38 × 4

= $45.52

Cost of bike glove = $31.41

Cost of biking outfit = $57.75

Write an inequality to solve for the number of biking outfit Ethan can purchase

let

x = number of biking outfit Ethan can purchase

620 ≥ 427.57 + 45.52 + 31.41 + 57.75x

620 ≥ 504.5 + 57.75x

620 - 504.5 ≥ 57.75x

115.5 ≥ 57.75x

x ≥ 115.5 / 57.75

x ≥ 2

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1. This task would likely be framed as a supervised learning problem

2. This task would also be framed as a supervised learning problem.

3. This task would typically be framed as an unsupervised learning problem.

4. This task would likely be framed as a regression problem since the goal is to estimate the repair time,

5. This task can be considered as an unsupervised learning problem.

Deciding whether to issue a loan to an applicant based on demographic and financial data (with reference to a database of similar data on prior customers):

This task would likely be framed as a supervised learning problem. The goal is to predict whether to approve or reject a loan application based on the given data. Hence, it can be considered a classification problem.

In an online bookstore, making recommendations to customers concerning additional items to buy based on the buying patterns in prior transactions:

This task would also be framed as a supervised learning problem. The goal is to recommend additional items to customers based on their buying patterns. It can be approached as a recommendation system using collaborative filtering techniques, which involve predicting customer preferences. This can be considered a classification problem.

Identifying segments of similar customers:

This task would typically be framed as an unsupervised learning problem. The objective is to identify groups or clusters of similar customers based on their attributes or behaviors. Unsupervised learning algorithms such as clustering can be used to accomplish this task.

Estimating the repair time required for an aircraft based on a trouble ticket:

This task would likely be framed as a regression problem since the goal is to estimate the repair time, which is a continuous variable. Supervised learning techniques such as regression algorithms can be employed to predict the repair time based on the provided input features.

Automated sorting of mail by zip code scanning:

This task can be considered as an unsupervised learning problem. The aim is to sort mail based on zip codes, which involves grouping similar items together. Unsupervised learning algorithms like clustering can be utilized to identify patterns and group the mail accordingly.

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Answer:

AB ║DC

Step-by-step explanation:

According to the question, it is mentioned that

m∠3= m∠7

As it can seen that the alternate interior angles are equal also the lines i.e. corresponding would be parallel

So,

AB ║DC

This represent that AB is parallel to DC

AB is parallel to DC.

Hence, the same is to be considered

The above represent the answer and the same is relevant

Step-by-step explanation:

if you did not leave anything out, all we can do is

T = CB - 6

T + 6 = CB

C = (T + 6)/B

Answer:

y = -23x+225

Step-by-step explanation:

Bugdet=spending

225 is the y-intercept and 23 is the slope or amount spent per day.

Answer: x=14°

Step-by-step explanation:

All angles of a triangle added together is 180°. So we can add the angles together.

7x-11+5x-2+2x-3=180           [combine like terms]

14x-16=180                             [add both sides by 16]

14x=196                                  [divide both sides by 14]

x=14

Therefore, x=14°.

The probability that the last person to board gets to sit in their assigned seat is 1/50 or 0.02, which is 2%.

The probability that the last person to board gets to sit in their assigned seat can be determined by analyzing the possible seating scenarios.

Let's break down the problem step by step:

1. The first person, who has lost their boarding pass, chooses a random seat. There is a 1/100 probability that they choose their assigned seat correctly.

2. Now, there are two possibilities:

a. If the first person occupies their assigned seat, everyone else will also sit in their assigned seats, resulting in the last person sitting in their assigned seat. The probability of this scenario is 1/100.

b. If the first person occupies someone else's seat, we move to the next step.

3. From the second person onwards, if a person finds their assigned seat unoccupied, they will sit in it, ensuring that the last person also gets their assigned seat. This scenario has a probability of 1/100.

4. If a person finds their assigned seat occupied, they will choose another seat at random from the remaining unoccupied seats. This will continue until the last person boards.

Analyzing all the possible scenarios, we can see that either the first person sits in their assigned seat (1/100 probability) and everyone follows suit, or the first person sits in someone else's seat (99/100 probability), leading to a chain of random seat changes. In this case, the last person will only get their assigned seat if they happen to be the last person who needs to change their seat.

Since there are 99 people in between the first and the last person who need to change seats, the probability that the last person gets their assigned seat in this scenario is 1/99.

Combining the two possibilities:

Probability = (1/100) + ((99/100) * (1/99))

Probability = 1/100 + 1/100

Probability = 2/100

Probability = 1/50

Therefore, the probability that the last person to board gets to sit in their assigned seat is 1/50 or 0.02, which is 2%.

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The house's value decreases by $29,960. The current value of the house is $398,040. The solution has been obtained by using arithmetic operations.

What are arithmetic operations?

The four fundamental operations that can be used to express any real number are referred to as "arithmetic operations" in mathematics. The four operations that produce quotient, product, sum, and difference are division, multiplication, addition and subtraction, respectively.

We are given that a house on the market was valued at $428,000.

After several years, the value decreased by 7%.

So, the price decreases by

$428,000 * (0.07) = $29,960

Now, the current value of the house is

$428,000 - $29,960 = $398,040

Hence, the house's value decreases by $29,960 and the current value of the house is $398,040.

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Answer:

We get -2 < r < 3

Corresponding to the fourth choice

The fourth number line is the correct option

Step-by-step explanation:

-2 < 3r+4 < 13

We have to isolate r,

subtracting 4 from each term,

-2-4< 3r + 4 - 4 < 13 - 4

-6 < 3r < 9

divding each term by 3,

-6/3 < r < 9/3

-2 < r < 3

so, the interval is (-2,3)

or, -2 < r < 3

this corresponds to

The fourth choice (since there is no equality sign)

To find the dimensions of the second rectangular prism that will have the same surface area as the first one, we can use the formula for the surface area of a rectangular prism which is:

Surface Area = 2lw + 2lh + 2wh

where l is the length, w is the width, and h is the height of the rectangular prism.

For the first rectangular prism, we have:

l = 3 m w = 7 m h = 4 m

Surface Area = 2lw + 2lh + 2wh Surface Area = 2(3)(7) + 2(3)(4) + 2(7)(4) Surface Area = 42 + 24 + 56 Surface Area = 122 m²

To find the dimensions of the second rectangular prism that will have the same surface area as the first one, we can use this formula again and solve for one of the variables. Let’s solve for l:

Surface Area = 2lw + 2lh + 2wh 122 = 2l(w+h) + 2wh 122 = 2l(w+h) + w(4) 122 = 2l(w+h) + 4w 118 = l(w+h)

Now we can choose any value for w and h and solve for l. Let’s choose w=1 and h=1:

118 = l(1+1) 118 = l(2) l = 59

So the dimensions of the second rectangular prism that will have the same surface area as the first one are:

l = 59 m w = 1 m h = 1 m

The maximum value of the data is given as follows:

75.

A box and whisker plot shows these five metrics from a data-set, listed and explained as follows:

The maximum value on the box plot is the end of the plot, hence it is of 75.

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After the additional registrations, there were 100 more voters registered as Democrats than as Republicans in the district by using the concept ratio.

Let's assume the initial number of registered Republicans in the district is 3x, and the initial number of registered Democrats is 5x.

According to the given information, the ratio of Republicans to Democrats before the additional registrations was 3/5. Therefore, we have the equation:

(3x + 600) / (5x + 500) = 3/5

To solve this equation, we can cross-multiply:

5(3x + 600) = 3(5x + 500)

15x + 3000 = 15x + 1500

By subtracting 15x from both sides, we get:

3000 = 1500

This equation is inconsistent and cannot be satisfied. This means there is no valid solution based on the given information. However, if we assume the ratio before the additional registrations was 5/3 instead of 3/5, we can solve the equation:

(3x + 600) / (5x + 500) = 5/3

Cross-multiplying again:

3(3x + 600) = 5(5x + 500)

9x + 1800 = 25x + 2500

Simplifying and rearranging the equation:

16x = 700

x = 700/16 ≈ 43.75

Now we can find the number of registered Democrats and Republicans after the additional registrations:

Democrats: 5x + 500 = 5(43.75) + 500 ≈ 319.75

Republicans: 3x + 600 = 3(43.75) + 600 ≈ 331.25

The difference between the number of registered Democrats and Republicans is:

319.75 - 331.25 ≈ -11.5

Since we're only interested in the absolute difference, the result is approximately 11.5 voters. Thus, there were approximately 11.5 more voters registered as Republicans than as Democrats after the additional registrations.

Based on the given information, there is no valid solution that satisfies the ratio of 3/5 after the additional registrations. However, if we assume the ratio was 5/3, then there were approximately 11.5 more voters registered as Republicans than as Democrats after the registrations.

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Answer:

N/A

Step-by-step explanation:

the question is not in depth could you add a photo

Answer:

Ok, so first, at the end of the equation, It says "+ 4" , right? So you put a point on positive 4 on the y-axis (the one that goes up and don, the vertical line.). Then, 2x means that's your slope, but since your graph only goes up to five, you gotta count down ward. So, go down from your point on the y-axis (4) twice and over to the LEFT (<--) once. Plot your point where you end up. then use a straightedge like a ruler, and connect your two points on the graph, and you have your line!

Hope this helps!

Answer:

it is cubix 12

Step-by-step explanation:

yw hope it helps!

For each of the given models, we will calculate the long-run effect of a one-time, one unit jump in xt​ on y.

a) The long-run effect of xt​ on y in Model 3a is 1.2.

b) The long-run effect of xt​ on y in Model 3b is 0.6.

c) The long-run effect of xt​ on y in Model 3c is not directly identifiable.

In Model 3a, the coefficient of xt​ is 1.2. This means that a one unit increase in xt​ leads to a 1.2 unit increase in y in the long run. The coefficient represents the long-run effect because it captures the average change in y when xt​ changes by one unit, holding other variables constant.

In Model 3b, the coefficient of xt​ is 0.6. This means that a one unit increase in xt​ leads to a 0.6 unit increase in y in the long run. The presence of the lagged variable xt−1​ suggests that there might be some dynamics at play, but in the long run, the effect of the current value of xt​ on y is 0.6.

In Model 3c, there is a feedback loop as yt−1​ appears on the right-hand side. This makes it difficult to isolate the direct long-run effect of xt​ on y. The coefficient of xt​, which is 0.6, represents the contemporaneous effect, but it does not capture the long-run effect alone. To quantify the long-run effect, additional techniques such as dynamic simulations or instrumental variable approaches may be required.

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The probability of landing heads exactly 11 times when a coin is tossed 20 times is option a) 0.1602

The repeated tossing of a coin follows a binomial distribution

P(X = x) = ⁿCₓ pˣ (1 - p)⁽ⁿ ⁻ ˣ⁾

where,

n = No. of times the experiment was repeated

x = random variable defining the number of "successes"

p = probability of "success"

Here

"succeess" is the event of landing a head.

n = 20

x = no. of times heads should show, i.e 11

p = probability of landing a head in a single toss

= 1/2

Hence, putting all this in the formula above we get

P(X = 11) = ²⁰C₁₁ 0.5¹¹ (1 - 0.5)⁽²⁰ ⁻ ¹¹⁾

= ²⁰C₁₁ 0.5¹¹ 0.5⁹

= ²⁰C₁₁ 0.5²⁰

= 20!/ 11! (20 - 11)! X 0.5²⁰

= a) 0.1602

Complete Question

An unbiased coin is tossed 20 times.

Find the probability that the coin lands heads exactly 11 times

a. 0.1602

b. 0.5731

c. 0.2941

d. 0.1527

e. 0.6374

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